How to Calculate the Surface Area of a Prism | Step-by-Step Guide with Formulas

Surface Area of a Prism

The surface area of a prism is the total area of all its faces

The surface area of a prism is the total area of all its faces. To find the surface area, you need to add up the areas of all the individual faces.

For a general prism, which has two congruent parallel bases and rectangular faces connecting the corresponding edges of the bases, you can calculate its surface area using the following formula:

Surface area = 2(Area of base) + Perimeter of base × Height

Here’s a breakdown of the steps to calculate the surface area of a prism:

1. Determine the shape of the base: The base of a prism can vary, but it is usually a polygon (such as a rectangle, triangle, or hexagon). Identify the shape of the base and find its area.

2. Calculate the area of the base: Depending on the shape of the base, use the appropriate formula to find its area. For example, if the base is a rectangle, the area is simply the product of its length and width.

3. Find the perimeter of the base: Measure or calculate the length of all the sides of the base, and then add them together to find the perimeter.

4. Determine the height of the prism: The height is the perpendicular distance between the two bases. It can usually be easily measured or given as part of the problem.

5. Calculate the surface area: Plug the values obtained from steps 2, 3, and 4 into the formula mentioned earlier. Multiply the area of the base by 2, then add the product of the perimeter of the base and the height.

It’s important to note that if the prism has more than one type of base (e.g., a triangular base on one side and a rectangular base on the other), you would need to calculate the area and perimeter for each base separately, and then add up the results.

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